One way to make the networks equivariant or invariant is to simply train them on more data. One could take the training dataset and augment it with translated, rotated and reflected versions of the original images. This approach however is undesirable: invariance or equivariance is still not guaranteed and the training takes longer. It would be better if the networks are inherently invariant or equivariant by design. This avoids a waste of network-capacity, guarantees invariance or equivariance, and increases performances, see for example [1]}.
